Fundamental Equations of Quantum Mechanics in Time-Varying Domain

Fundamental equations of quantum mechanics in time-varying domain are presented. The used method consists in transforming the variable domain into a fixed domain. The transformation has to be covariant in relation to the wavefunction. The new fundamental equations turn out to be a generalization of the classical equations established in a Newtonian space-time. When the time-varying domain becomes stationary, we find again the fundamental equations of the classical quantum mechanics.